dorsal/arxiv
View SchemaCoherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications
| Authors | Bindu A. Bambah, G. S. Agarwal |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9604025 |
| URL | https://arxiv.org/abs/quant-ph/9604025 |
| Journal | Invited talk published in "Proc. of the fourth int. conf. on Squeezed States and Uncertainty Relations", NASA Conf. Pub.3322.(1995) |
Abstract
We introduce and study the properties of a class of coherent states for the group SU(1,1) X SU(1,1) and derive explicit expressions for these using the Clebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the discrete series representations of SU(1,1). These are the generalization of the `Barut Girardello' coherent states to the Kronecker Product of two non-compact groups.The resolution of the identity and the analytic phase space representation of these states is presented. This phase space representation is based on the basis of products of `pair coherent states' rather than the standard number state canonical basis. We discuss the utility of the resulting `bi-pair coherent states' in the context of four-mode interactions in quantum optics.
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"abstract": "We introduce and study the properties of a class of coherent states for the\ngroup SU(1,1) X SU(1,1) and derive explicit expressions for these using the\nClebsch-Gordan algebra for the SU(1,1) group. We restrict ourselves to the\ndiscrete series representations of SU(1,1). These are the generalization of the\n`Barut Girardello\u0027 coherent states to the Kronecker Product of two non-compact\ngroups.The resolution of the identity and the analytic phase space\nrepresentation of these states is presented. This phase space representation is\nbased on the basis of products of `pair coherent states\u0027 rather than the\nstandard number state canonical basis. We discuss the utility of the resulting\n`bi-pair coherent states\u0027 in the context of four-mode interactions in quantum\noptics.",
"arxiv_id": "quant-ph/9604025",
"authors": [
"Bindu A. Bambah",
"G. S. Agarwal"
],
"categories": [
"quant-ph"
],
"journal_ref": "Invited talk published in \"Proc. of the fourth int. conf. on\n Squeezed States and Uncertainty Relations\", NASA Conf. Pub.3322.(1995)",
"title": "Coherent States for Kronecker Products of Non-Compact Groups: Formulation and Applications",
"url": "https://arxiv.org/abs/quant-ph/9604025"
},
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